A Multi-step Dynamics Modeling Framework For Autonomous Driving In Multiple Environments

Authors: Jason Gibson, Bogdan Vlahov, David Fan, Patrick Spieler, Daniel Pastor, Ali-akbar Agha-mohammadi, Evangelos A. Theodorou · ICRA 2023

Licences

Open Access
Paper: CC BY 4.0

Everything below draws on the full paper under its CC BY 4.0 licence; its figure is credited to the authors.

TL;DR

Initialized LSTMs inside a physics-based hybrid model, trained with an integrated position loss, predict 5 s off-road vehicle trajectories in real time for GPU MPPI control.

Why it matters

The model runs inside MPPI with 18,432 samples on one RTX 3080 and stays usable at twice its training horizon, which is what a planner for fast off-road driving needs. Because labels come only from odometry, cheaper human driving logs can be used alongside autonomous data. The comparison also shows that keeping simple parametric actuator models inside the learned model prevents large errors once the network sees inputs it was not trained on.

Problem

Sampling-based model predictive controllers such as MPPI need dynamics models that are both accurate and cheap, since they run millions of forward predictions per second. Models trained on single-step prediction are rolled out recursively, so small errors compound over the horizon, and slow effects are treated as noise. Off-road driving adds hard-to-model terrain interaction and large actuator delays on steering and braking.

Proposed solution

The vehicle model is split into learned actuator-delay models for brake and steering (a rate-limited first-order lag plus a small network) and engine and terrain-drag networks inside kinematic equations. Each learned part is an LSTM whose hidden and cell states are set by a separate initializer network run once on past data, so all MPPI samples reuse it. Training uses an integrated loss on predicted positions over a fixed 5 s horizon, which needs only smooth odometry as labels and allows human and autonomous driving data to be mixed.

Key insights

Training over a fixed horizon removes the need for long-term LSTM stability, yet the models stayed stable at 10 s, twice the 5 s training horizon
The initializer network only sees past data, so it runs once on the CPU and its hidden state is shared by every sampled trajectory on the GPU
An integrated position loss lets the networks output quantities with no direct labels, such as wheel-frame drag forces, and avoids differentiating noisy odometry
Parametric brake and steering delay models with a learned correction beat pure black-box delay networks, whose errors pushed the dynamics networks into unseen inputs
A shared engine, steering and brake model with a terrain-drag network switched per environment covered both desert and chaparral data

Main results

Dataset of about 650,000 trajectories from two environments: Helendale (≈300,000 human, ≈100,000 autonomous) and Paso Robles (≈100,000 human, ≈150,000 autonomous); training set ≈500,000 and test set ≈150,000
With ground-truth actuator states (combined data), learned models reached about 5 m distance error at t = 10 s (e.g. HI-LSTM 4.981 ± 17.143 m) against 11.153 ± 77.551 m for the parametric baseline
Full system on autonomous data at t = 5 s: HI-LSTM 2.089 ± 3.463 m and 0.145 rad yaw error, against 7.259 ± 28.837 m and 0.775 rad for the kinematic K-LSTM
Full system at t = 10 s: HI-LSTM 5.722 ± 22.936 m against 21.015 ± 155.293 m for KI-LSTM
One MPPI iteration with 18,432 samples on an RTX 3080 took 59.346 ms and 38.08 kB of CUDA memory for the hybrid models, against 83.708 ms and 62.468 kB for the kinematic networks and 23.327 ms for the parametric model
Black-box steering networks had about 2× the average steering error of their parametric counterparts

Limitations

Predictions can be non-smooth in the first couple of steps while still giving low loss; the authors call this an ongoing problem
For engine and terrain modeling alone, the hybrid architecture did not improve accuracy significantly over pure learned networks, and the initializer network had a limited effect
The environment class (desert, wooded area) is assumed known in advance and the matching terrain network is loaded at run time
The method is sensitive to odometry drift and small jumps, which produced short dynamically infeasible trajectories near zero velocity and over-smoothed outputs
Validated on one vehicle in two environments; the validation and test sets were drawn from the same day of testing

Field impact

Finalist for the ICRA 2023 Outstanding Planning Paper award, with 26 citations. The paper provides a supplementary video; it does not state a code or dataset release.

Abstract

Modeling dynamics is often the first step to making a vehicle autonomous. While on-road autonomous vehicles have been extensively studied, off-road vehicles pose many challenging modeling problems. An off-road vehicle encounters highly complex and difficult-to-model terrain/vehicle interactions, as well as having complex vehicle dynamics of its own. These complexities can create challenges for effective high-speed control and planning. In this paper, we introduce a framework for multistep dynamics prediction that explicitly handles the accumulation of modeling error and remains scalable for sampling-based controllers. Our method uses a specially-initialized Long Short-Term Memory (LSTM) over a limited time horizon as the learned component in a hybrid model to predict the dynamics of a 4-person seating all-terrain vehicle (Polaris S4 1000 RZR) in two distinct environments. By only having the LSTM predict over a fixed time horizon, we negate the need for long term stability that is often a challenge when training recurrent neural networks. Our framework is flexible as it only requires odometry information for labels. Through extensive experimentation, we show that our method is able to predict millions of possible trajectories in real-time, with a time horizon of five seconds in challenging off road driving scenarios.

Open Source Robotics